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Acquisitions - Narrative (Details)
$ in Millions
9 Months Ended
May 31, 2020
USD ($)
Sep. 17, 2019
brand
Aug. 31, 2019
USD ($)
May 31, 2019
USD ($)
Aug. 31, 2018
USD ($)
Business Acquisition [Line Items]          
Goodwill $ 1,086.4   $ 967.3 $ 964.1 $ 970.6
The Luminaires Group (TLG)          
Business Acquisition [Line Items]          
Number of niche lighting brands | brand   5      
Fiscal 2020 Acquisitions          
Business Acquisition [Line Items]          
Goodwill 127.5        
Identified intangible assets $ 180.7        
Weighted average useful life of acquired intangible assets 16 years